According to Karwarth in the Journal of the Institute of Navigation, Vol 24, No. 1, pp. 105-120, Jan. 1, 1971, the basic objective of area navigation is to position in real time with appropriate accuracy one or more mobile platforms with reference to some known coordinate system. The number of coordinates needed depends upon whether the course of the mobile platform can be charted on a known surface or must be described in three-dimensional space as in the respective cases of a ship at sea and an aircraft. The ability to chart a course based on past, present and future desired positions in a principal element in distinguishing an area navigation system from navigation using point-to-point or "homing" approaches such as VOR/DME (VHF Omnidirectional Range/Distance Measuring Equipment).
Positions are established in all cases by signal transmission between the mobile units and at least one transmitter of known location. The transmissions can be electromagnetic (including optical) or acoustic in any medium including air. Two basic methods are normally used to obtain positions:
Positions may be determined from a sufficient number of range measurements to known reference locations by using what is commonly known as "range-range" systems, or positions may be determined from a sufficient number of range differences to known reference locations, by using what is commonly known as "hyperbolic" systems. In each case a sufficient number is at least equal to the number of coordinate values needed.
Direct ranging involves calculation of intersections of the circles or spheres of uniform range from each reference location to the mobile unit. By contrast, the locus of equal range difference from the mobile unit to a pair of reference locations are hyperbolae or hyperboloids of revolution. Again, positions are calculated by intersection of curves or surfaces, but in this case related to the hyperbolae, hence the name hyperbolic systems.
An exemplary task of area navigation might be the positioning of a ship at near shore distances. In range-range operation only two shore stations are needed while a hyperbolic system requires three. Three shore stations admit calculation of two independent range differences. As a general rule, hyperbolic systems offset a disadvantage in requiring one or more known reference location than the simpler range system by not requiring either a time standard or an active transmitter on the ship.
As for the transmitted signals, a variety of differing modes of operation are possible. Ranges can be determined from signal transmission time between the mobile unit and a reference location if the signal initiation time is known, a time standard is available, and a signal propagation velocity is also known. The simplest means for establishing known initiation times is to transmit signals only in response to some interrogation. Alternatively, if transmissions are synchronized to occur at regular time intervals, time differences are readily determined, with no interrogation step needed, using only a local clock and a propagation velocity.
Again, signal transmissions themselves can consist of continuous waveforms (typically sinusoids), intervals of continuous signal transmissions, or sequences of pulses. The choice of transmitted signal reflects consideration of the information desired, mode of operation (range-range versus hyperbolic), noise effects, and the extent of Doppler distortions among other factors.
Continuous waveforms are the most robust signals in the presence of noise backgrounds since correlation-type receivers may take advantage of the extreme signal duration. Such signals have no resolution in time and are used principally with hyperbolic systems to establish time-differences by making phase comparisons with reference signals. Where the transmitter-receiver relative velocity is not insignificant in proportion to the signal propagation velocity, Doppler effects shift the frequencies of continuous waveforms. Frequency shifts may be viewed as errors since they distort subsequent correlation steps and thus degrade phase comparisons; however, if such shifts are measured, they do relate to velocity information should this be desired.
Use of continuous signals over intervals provides time resolution as well as opportunities for correlation detection, but over shorter data windows. Again, any Doppler effects may be viewed either as constituting an error in range determination or if measured, velocity information. The tolerance of such signals to noise effects is of course diminished in direct relation to their shortened duration.
In the limit, as duration is shortened, pulsed signals must be considered which when taken individually offer no opportunity to measure Doppler effects. Hence significant transmitter-receiver relative velocities will be noted as range errors for such systems. These signals are also most affected by the presence of noise, but afford the greatest resolution in making a direct time measurement.
It follows that the alternative methods of operation that exist constitute attempts at optimizing a number of trade-offs which interact with some complexity. The hardware requirement, operations costs, efficiencies and effectiveness in terms of achievable accuracy are all essential ingredients that play roles in the optimization. Navigation systems based on the present invention may generally serve as replacements for such systems and others.
The present invention involves the application of dispersion to signal phase. The phenomenon of dispersion is well known in optics. By way of an appropriate background regarding this principle in order to understand its application to the present invention, an appropriate definition of dispersion, a presentation of the distinguishing characteristics of normal and anomalous dispersion, and a description of various embodiments of dispersion may be found in Sommerfeld, Mechanics of Deformable Bodies, Academic Press, New York 396 p, 1950 (see in particular pp. 172-206, 2nd printing 1956), and Longhurst, Geometrical and Physical Optics, Longman, 592 p, 2nd Edition, 1967 (see in particular p. 452 and FIG. 20-4).
It is necessary to distinguish also the phase-angle rotation undergone by a signal in traveling through a dispersive medium or in post-critical angle reflection from a mere time delay. If the angular frequencies contained within the spectrum of a signal having bandwidth range from a value .omega..sub.1 to a greater value .omega..sub.2, the phase spectrum of the signal over that range will be some function f(.omega.), .omega..sub.1 .ltoreq..vertline..omega..vertline..ltoreq..sub.2. After traveling through a dispersive medium the change in phase of the signal, which characterizes the degree of dispersion, can be described in first approximation by .DELTA.f(.omega.)=.theta..sub.1 +.theta..sub.2 .omega. where .theta..sub.1 and .theta..sub.2 are constants which depend only on the medium and the distance travelled within the medium.
The value of the constant .theta..sub.2 describes the delay of the signal, that is, it is the increment of time that the signal has undergone in traveling through the medium of simply the signal travel time. The phase angle rotation is given by the value of the constant .theta..sub.1. Because phase is an angular measure, two signals of like amplitude spectra whose phase spectra differ by an integral multiple of 2.pi. are identical and hence indistinguishable. It is therefore customary to replace any value of .theta..sub.1 that is equal to or greater than 2.pi. by the residue of .theta..sub.1 modulo 2.pi. or in common terminology by the remainder after dividing .theta..sub.1 by 2.pi.. Values of .theta..sub.1 modulo 2.pi. other than 0 and .pi. correspond to changes in the signal shape.